A368322 - OEIS

%I #10 Dec 21 2023 10:24:03

%S 1,5,37,389,5413,94085,1962277,47746949,1327769893,41538664325,

%T 1443908686117,55210237509509,2302968844974373,104068337416767365,

%U 5064468256286449957,264065894676248072069,14686540175450593986853,867871886679723760867205

%N Expansion of e.g.f. exp(2*x) / (4 - 3*exp(x)).

%F a(n) = 2^n + 3 * Sum_{k=1..n} binomial(n,k) * a(n-k).

%F a(n) = (16/9)*A032033(n) - (1/3)*(1 + (4/3)*0^n).

%o (PARI) b(n, t) = sum(k=0, n, t^k*k!*stirling(n, k, 2));

%o a(n, m=2, t=3) = my(u=1+1/t); u^m*b(n, t)-(1/t)*sum(j=0, m-1, u^j*(m-1-j)^n);

%Y Cf. A032033, A201354, A368323, A368324.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 21 2023